Unified Gauss–Markov Modeling of Ionospheric Residuals for Spatiotemporal Cohesive Characterization

Abstract

Ionospheric residuals from empirical models exhibit strong spatiotemporal correlations, posing a dominant error that undermines the integrity and robustness of single-frequency Global Navigation Satellite System (GNSS) applications, for example, in the aviation industry. This study develops a unified Gauss–Markov (GM) framework to characterize these correlations. Physically motivated by the finite-memory property and exponential correlation decay of ionospheric variations, the GM model captures both temporal and spatial dependencies using a shared exponential form, while a joint model examines their coupling. The differential operation is introduced to remove bias and large-scale trends for improved parameter estimation. Two parameter estimation methods are introduced: one based on the normalized exponential correlation function decaying to $1/e$ , and another using slope fitting with an approximate linear function through Taylor expansion. This unified exponential structure coherently captures interdependent ionospheric variations in both spatial and temporal domains, thereby facilitating unified correlation analysis and supporting enhanced error modeling, residual interpolation, and integrity monitoring. It also clarifies the physical and mathematical rationale for constructing a cohesive spatiotemporal residual model, while showing that the classical kriging covariance is recovered as a spatial-only special case. Analysis of the September 2017 geomagnetic storm reveals that correlation time and distance significantly decrease during disturbances, indicating faster residual decorrelation and weakened horizontal coherence. Temporal–zonal equivalence and diurnal analyses further show local time (LT) coupling and day–night changes in spatial coherence, while target-ionospheric pierce point (IPP) validation further supports the effectiveness of the proposed spatiotemporal GM model.